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Question
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
Solution
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
(f ° g) (x) = f(g(x)) = `"f"(x/(1 - x))`
= `(x/(1 - x))/(x/(1 - x) + 1)`
= `x/(x + 1 - x)`
= x
(g ° f) (x) = g(f(x))
= `"g"(x/(x + 1))`
= `(x/(x + 1))/(1 - x/(x + 1))`
= `x/(x + 1 - x)`
= x
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